7th US Army Conference on Applied Statistics

                 22-26 October 2001
                    Santa Fe, NM



Title:	On a New Approach to Robust Estimation

		David W. Scott
		Noah Harding Professor of Statistics
		Rice University
		Houston, TX  77251-1892

		scottdw@rice.edu
		713-348-6037
		713-348-5476 (Fax)


Abstract:


	In this talk, I describe an alternative approach to
	robust estimation.  Robust estimation provides a
	powerful solution to practical problems in applied
	statistics.  Simple tasks such as data cleaning may
	be prohibitively expensive with large datasets.  These
	techniques may also handle the difficult situation
	where a dataset contains large clusters of outliers.

	In order to use a robust estimation algorithm
	(such as the M-estimator described by Hampel and
	Huber), the shape and scale of the influence
	function must be specified.  Tukey's biweight
	function is a popular choice but there are many,
	many possibilities.  The scale may be determined
	by a simple robust method (such as the interquartile
	range), or by iteratively reweighting the data.

	In our approach, maximum likelihood is replaced
	by a data-based minimum-distance criterion.
	I show that the specification of the shape and
	scale of the influence function can be replaced
	by a single choice of a distribution function for
	the data.  This idea is illustrated for several
	common choices of data, including Gaussian.

	This framework works well in both density and
	regression problems.  Groups of multivariate
	outliers may be readily identified.  Experimental
	design with messy data is facilitated.
	Semiparametric models such as mixtures of normals
	also fall within this paradigm.  Several case
	studies are presented and actual code given.